Respuesta :
a. The new expression that is showing the distributive division for each of the 12 parts is 3p – 4
b. The equation of length of each 12 equal division of pipes using the distributive property of division is 3p – 4
Given: Expression 36p – 48 representing the total distance of piping.
To simplify for the portions the needs to divide the pipe into 12 equal halves.
What is the distributive Property of division?
The distributive property of division states that for a division if we divide the numerator or the dividend into smaller parts that are exactly divisible by the denominator or the divisor respectively, and then add all the quotients of the smaller divisions then the answer will be exactly same as dividing the larger number without breaking into smaller parts.
Let’s solve the given question:
The total distance of piping = 36p – 48
a. Now total distance of piping will have to be divided into 12 equal parts.
Let’s say the equation of the sizes of each part be x
Then the sum of all the 12 parts will be equal to 36p – 48
So x + x + …. 12 times = 36p – 48
=> 12x = 36p – 48
Dividing both sides by 12:
12x / 12 = (36p – 48) 12
x = 3p – 4
The new expression that is showing the distributive division for each of the 12 parts is 3p – 4
b. We have to use the Distributive property to show the division of piping for her job
Now the pipe of length 36p – 48 has to be divided into 12 equal parts
So length of each part is (36p – 48) / 12
We can write 36p – 48 as {(12p – 24) + (24p – 12)}
So (36p – 48) / 12 = {(12p – 24) + (24p – 12)} / 12
= (12p – 24) / 12 + (24p – 24) / 12
= 12p / 12 – 24 / 12 + 24p / 12 – 24 / 12
= p – 2 + 2p – 2
= 3p – 4
So the equation of length of each 12 equal division of pipes is 3p – 4
Hence
a. The new expression that is showing the distributive division for each of the 12 parts is 3p – 4
b. The equation of length of each 12 equal division of pipes using the distributive property of division is 3p – 4
Know more about “distributive property” here: https://brainly.com/question/5637942
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